# On a class of conformally invariant semi basic vector one forms

## TL;DR

This paper introduces a new class of conformally invariant semi-basic vector one-forms on Finsler manifolds, characterizes associated conservative connections, and explores their geometric properties and correspondences.

## Contribution

It defines conservative semibasic vector 1-forms, characterizes conservative L-Ehresmann connections, and establishes a correspondence with torsion-free semibasic vector forms, advancing Finsler geometry theory.

## Key findings

- Characterization of conservative L-Ehresmann connections
- Establishment of a correspondence between torsion-free forms and vertical vector fields
- Construction of semisprays generating the Ehresmann connections

## Abstract

In this paper, we define conservative semibasic vector $1-$forms on the tangent bundle of a Finsler manifold. Using these vector $1-$forms, we characterize conservative $L-$Ehresmann connections with respect to the energy function. Then we find a correspondence between torsion-free semibasic vector $1-$forms and the subset of vertical vector fields. Taking into account this correspondence, we construct a class of semisprays that generates the Ehresmann connections mentioned above.